Details

Time bar (total: 7.8s)

sample35.0ms

Algorithm
intervals
Results
8.0ms256×pre80true
8.0ms256×body80valid

simplify369.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
099
1179
2539
31449
43079
54619
65219
75229
done5229

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.7b

localize12.0ms

Local error

Found 2 expressions with local error:

0.4b
(+ b (+ c d))
2.9b
(+ a (+ b (+ c d)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity add-log-exp
9×sum-log distribute-lft-out
2×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt associate-+r+ flip3-+ add-cbrt-cube flip-+
Counts
2 → 32
Calls
2 calls:
17.0ms
(+ b (+ c d))
70.0ms
(+ a (+ b (+ c d)))

series64.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(+ b (+ c d))
46.0ms
(+ a (+ b (+ c d)))

simplify645.0ms

Counts
38 → 38
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
056350
1171321
2815307
done5000307

prune173.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.4b

localize10.0ms

Local error

Found 1 expressions with local error:

2.9b
(+ a (+ (+ b c) d))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
6×sum-log distribute-lft-out
1×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt associate-+r+ flip3-+ add-cbrt-cube flip-+
Counts
1 → 17
Calls
1 calls:
101.0ms
(+ a (+ (+ b c) d))

series39.0ms

Counts
1 → 3
Calls
1 calls:
39.0ms
(+ a (+ (+ b c) d))

simplify1.7s

Counts
20 → 20
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
039207
1113195
2471181
33323181
done5001181

prune110.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.2b

localize19.0ms

Local error

Found 2 expressions with local error:

0.6b
(cbrt (pow (+ a (+ (+ b c) d)) 3))
2.9b
(+ a (+ (+ b c) d))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
32×*-un-lft-identity
18×cbrt-prod distribute-lft-out
11×add-log-exp
6×unpow-prod-down cube-prod sum-log
5×add-sqr-sqrt add-cube-cbrt
2×pow1 add-exp-log cube-div cbrt-div flip3-+ add-cbrt-cube flip-+
1×+-commutative cube-mult associate-+r+ pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
2 → 46
Calls
2 calls:
160.0ms
(cbrt (pow (+ a (+ (+ b c) d)) 3))
84.0ms
(+ a (+ (+ b c) d))

series114.0ms

Counts
2 → 6
Calls
2 calls:
67.0ms
(cbrt (pow (+ a (+ (+ b c) d)) 3))
47.0ms
(+ a (+ (+ b c) d))

simplify988.0ms

Counts
52 → 52
Iterations

Useful iterations: 2 (134.0ms)

IterNodesCost
082767
1230586
21453548
done5001548

prune275.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.6b
(cbrt (pow (+ (+ d (+ b c)) a) 3))
0.6b
(cbrt (pow (cbrt (pow (+ (+ d (+ b c)) a) 3)) 3))
2.9b
(+ (+ d (+ b c)) a)

rewrite573.0ms

Algorithm
rewrite-expression-head
Rules
102×cbrt-prod
78×*-un-lft-identity
42×distribute-lft-out
39×unpow-prod-down cube-prod
15×add-sqr-sqrt add-cube-cbrt
12×add-log-exp
6×cube-div cbrt-div sum-log
4×cube-mult unpow3 sqr-pow
3×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
2×pow1/3 rem-cbrt-cube
1×+-commutative associate-+l+
Counts
3 → 105
Calls
3 calls:
143.0ms
(cbrt (pow (+ (+ d (+ b c)) a) 3))
257.0ms
(cbrt (pow (cbrt (pow (+ (+ d (+ b c)) a) 3)) 3))
167.0ms
(+ (+ d (+ b c)) a)

series181.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(cbrt (pow (+ (+ d (+ b c)) a) 3))
71.0ms
(cbrt (pow (cbrt (pow (+ (+ d (+ b c)) a) 3)) 3))
37.0ms
(+ (+ d (+ b c)) a)

simplify694.0ms

Counts
114 → 114
Iterations

Useful iterations: 2 (220.0ms)

IterNodesCost
01282293
13801482
215991361
done50021361

prune281.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01111
1189
2199
done199

end0.0ms

sample1.1s

Algorithm
intervals
Results
339.0ms8000×body80valid
269.0ms8000×pre80true